Consider the following statements about the refraction of light waves:
(A) To find the refracted wavefront, secondary wavelets of radius \(v_2\tau\) are drawn in the second medium, where \(v_2\) is the speed of light in that medium.
(B) If the refracted wave bends towards the normal, light travels faster in the second medium.
(C) When a wave is refracted into a denser medium, its frequency decreases.
(D) For angles of incidence greater than the critical angle, there is no refracted wave.
Which of the above statements are incorrect?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (B) and (C) only
In the wave picture, the speed of light in each medium decides how the wavefront bends. A wave slows down in a denser medium and bends towards the normal.
(A) To find the refracted wavefront, secondary wavelets of radius \( v_2\tau \) are drawn in the second medium. — Correct statement. In time \( \tau \) the wave covers a distance \( v_2\tau \) in the second medium. So the wavelet there has this radius.
(B) If the refracted wave bends towards the normal, light travels faster in the second medium. — Incorrect statement. From \( \sin i/\sin r=v_1/v_2 \), a smaller angle \( r \) gives \( v_2\lt v_1 \). Light is slower in the second medium. Faster light was the prediction of the corpuscular model.
(C) When a wave is refracted into a denser medium, its frequency decreases. — Incorrect statement. The wavelength and the speed decrease. The frequency stays the same as that of the incident wave.
(D) For angles of incidence greater than the critical angle, there is no refracted wave. — Correct statement. At \( i=i_c \) the angle of refraction is \( 90^\circ \). For larger angles no refracted wave exists, and total internal reflection takes place.
NCERT (2026-27):
Refraction of a plane wave – “… In order to determine the shape of the refracted wavefront, we draw a sphere of radius v2τ from the point A in the second medium (the speed of the wave in the second medium is v2). …”
Refraction of a plane wave – “… From the above equation, we get the important result that if r < i (i.e., if the ray bends toward the normal), the speed of the light wave in the second medium (v2) will be less then the speed of the light wave in the first medium (v1). This prediction is opposite to the prediction from the corpuscular model of light and as later experiments showed, the prediction of the wave theory is correct.”
Refraction of a plane wave – “The above equation implies that when a wave gets refracted into a denser medium (v1 > v2) the wavelength and the speed of propagation decrease but the frequency ν(= v/λ) remains the same.”
Refraction at a rarer medium – “… Obviously, for i > ic, there can not be any refracted wave. …”